{
  "id": "math/0504057",
  "version": "v1",
  "published": "2005-04-04T15:34:01.000Z",
  "updated": "2005-04-04T15:34:01.000Z",
  "title": "The Hardy inequality and Nonlinear parabolic equations on Carnot groups",
  "authors": [
    "Ismail Kombe"
  ],
  "comment": "12 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we shall investigate the nonexistence of positive solutions for the following nonlinear parabolic partial differential equation:\\[ \\begin{cases} \\frac{\\partial u}{\\partial t}= \\Delta_{\\mathbb{G},p}u+V(x)u^{p-1} & \\text{in}\\quad \\Omega \\times (0, T), \\quad 1<p<2, u(x,0)=u_{0}(x)\\geq 0 & \\text{in} \\quad\\Omega, u(x,t)=0 & \\text{on}\\quad \\partial\\Omega\\times (0, T) \\end{cases} \\] where $ \\Delta_{\\mathbb{G},p}$ is the $p$-sub-Laplacian on Carnot group $ \\mathbb{G}$ and $V\\in L_{\\text{loc}}^1(\\Omega)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-04-04T15:34:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K65",
      "35R05",
      "22E30",
      "26D10"
    ],
    "keywords": [
      "nonlinear parabolic equations",
      "carnot group",
      "hardy inequality",
      "nonlinear parabolic partial differential",
      "nonexistence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......4057K"
    }
  }
}